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A process that takes millions of years can't be directly observed. However, there have been several observed speciation events in lab experiments including in Drosophila (fruit fly) species. IIRC, There is also evidence of early-stage speciation in events in Anoles and a species of Australian lizard whose names elude me at the moment.
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Chinmay KanchiFeb 3 '14 at 20:28

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The definition of evolution does not stipulate the manifestation of new species, it is only "descent with modification" - a change in traits along a lineage over time. The evolution of new species is called speciation. Check your definitions, that is all.
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GriffinEvoFeb 4 '14 at 7:23

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@LotusBiology There is no such thing as "vertical" and "horizontal" evolution, as separate processes. The movie is just a tendentious piece of propaganda, and every attempt of an honest answer is being cut-off or misrepresented.
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fileunderwaterFeb 4 '14 at 10:25

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This question appears to be off-topic because it is about Creationism.
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Jack AidleyFeb 5 '14 at 11:52

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What would you accept to consider being an observation? It seems to me that many creationist would accept to consider something to be an observation only if it is extremely simple to understand it. The methodology of observation in evolutionary biology (just like in most science field) are not always very simple to understand for non biologists.

The word "kind" is not define in the sentence "what is a change of kind?".

Because the question is poorly defined, it makes it impossible to answer. And that is the common problem with creationist arguments. Their arguments are not scientific and therefore cannot really been argued for or against. Just want to say also that evolutionary biologist do not need non-scientist to fight against their work. Scientists create their own criticism. Scientists do not form a political party that fight for one point of view just for the purpose of defending it. They think neutrally and objectively (as much as a human can).

Change of kind

If change of kind = change in DNA sequence

Let's assume change of kind means change in the DNA sequence. Change of kinds have been observed in real time in almost all lineages we looked at (including humans). These changes are not only observable at the genetic level but also at the so-called phenotypic (loosely speaking the phenotype is way the organism looks like) level. We can for example think of disease in humans that are due to de novo mutations.

If change of kind = a population/species adaptat to a new environment

If by change of kind, one mean "adaptation", then adaptation to new environment have been observed in tons of lineages again. In a lab it can be observed in bacteria within the course of a month. It has been observed in many mammals, birds, plants and unicellular eukaryotes.

If change of kind = one lineage splits and there is reproductive isolation

If by change of kind, one mean "reproductive isolation", then reproductive isolation has also been observed in real time and many times in nature and in labs (see this post for example)

If change of kind = something else... Just tell me what is this something else and we'll let you know if it has ever been observed

Observation

If you accept observation based on slightly more complex method such as molecular clocks and comparative genomics, then you'll find thousands of example of "change of kind", again in roughly speaking all lineages of the tree of life.

Very recently I worked on the speciation of clownfishes. This speciation was dated and we observed morphological and genetic adaptation to specific environments.

P.s. I haven't looked at the video completely but only some randomly selected part for a total duration of about 30 seconds! At first sight I'd like to say: Please don't fall into the trap of the media. One making interviews of people that are sometimes identified and sometimes not and that select for some part of their answer and that ask poorly defined question can really easily say anything from his records.

I welcome editing and I welcome anybody wanting to add references. One can find tons of them!

+1 for the second to last paragraph. I find it impossible to believe that P.Z.Myers, who makes his living partly by debunking creationists, would be unable to answer the question as posed.
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Chinmay KanchiFeb 4 '14 at 13:10

I don't know why we haven't labeled domestic dogs as different species. I know they are still technically capable of interbreeding, but in the wild I doubt chihuahuas and great danes are going to interbreed very well. All we have to do is define dogs as different species and we can point to that everytime the creationists ask for an example of a new species.
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user137Jan 12 at 1:58

It depends a lot on the meaning of "Kind." An ill-defined term is subject to goal-post-moving, so that if an example is presented of A splitting from B, or A descending from B, the person asking the question can claim that A and B are still the same "Kind". With a sufficiently broad definition of "Kind", you are just a funny kind of fish.

It can also be used as a strawman, to ask for evidence of a sort of evolution that nobody accepts, for example, the crocoduck.

Secondly, @GriffinEvo is absolutely correct that observable evidence does not have to be "live." Archaeologists for example can and do observe evidence of battles without ever being in combat. For a partial list of evidence for speciation and the common descent of different species from a common ancestor, see http://www.talkorigins.org/faqs/comdesc/.

So how does "vertical evolution" work Kevin? Tell me if this is wrong: So -common ancestor- population has a portion of it split off and go into a new environment, and another portion go somewhere else, and those two populations, if given enough time and environmental pressure, morph into a completely new kind? If so, why don't we see bacteria morph into something other than bacteria if they are put into a new environment? Given their quick reproduction?
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LotusBiologyFeb 4 '14 at 2:31

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@lotusbiology To go from a bacteria to something else, such as a simple multi celled organism, is a monumentally large step to try and observe.
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GriffinEvoFeb 4 '14 at 7:45

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@LotusBiology Because evolving from single cell to multi-cellular organisms is not a small but a huge step. It took quite a while (about 2 billions years after the first unicellular organisms occured). And: Evolution is taking place in bacteria, there is a nice experiment about it. See here.
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ChrisFeb 4 '14 at 8:16